22 



Blasius obtained a solution of Equations [13] for a flat plate, i.e., gf = 0, 

 in the form (see Reference 41 ): 



u = Uf'(Tj) [14] 



v = \\^- fof - f ) = f 7 (rif' - f) [15] 



n = y^ [16] 



where f (77) is the solution of the equation 



ff< + 2f m = .[17] 



Here, x is the distance from the leading edge of the plate, and the primes 

 indicate differentiation with respect to rj. Since the pressure distribution 

 in the neighborhood of a region likely to cavitate (at least on bodies of 

 fairly high length-diameter or length-beam ratios) is such as to approximate 

 the boundary conditions assumed above, the pressure across the boundary 

 layer should behave at least qualitatively as predicted from this solution. 

 Substituting the results [14] through [17] into the second of Equations [11], 

 the pressure gradient across the boundary layer is 



|| = lpU 2 R x " 1/2 f " [18] 



where 



R' 



-V? 



From the asymptotic expansion for the solution of [17] Blasius gives the value 

 f" = 0.332 for 17 = 0. Thus, 



f^>0 [19] 



across the boundary layer. It follows, therefore, that the pressure decreases 

 across the boundary layer toward the body. This result indicates that in un- 

 separated flows with a laminar boundary layer, cavitation will always occur at 

 the body and not outside the boundary layer. While the above result applies 

 to two -dimensional flows, and, thus, approximately, to thin struts, the same 

 result is obtained for bodies of revolution. In the latter case, it can be 

 shown that the pressure gradient across the boundary layer is not second order 



